Non-Convex Penalized Conditional Mean Subspace in Multivariate Regression

• Activity Number: 524
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Chongsun Park*+ and Jae Keun Yoo
• Companies: Sungkyunkwan University and Ewha Womans University
• Keywords: Central Mean Subspace ; Sparsity ; Non-convex Penalties

Abstract

Variable selection is fundamental to high dimensional modelling, including regression. A unified estimation strategy, which combines a regression-type formulation of sufficient dimension reduction methods and $L_1$ penalties proposed by Li (2007) turned out to be effective but fails to deliver a robust estimator. However, most of the sparse algorithms have problem in generalization to non-convex penalties since non-orthogonality cause difficulty in both investigation the performance in theory and solving computational problems. We propose a method for sparse solutions for conditional mean subspace in multivariate regression using thresholding based iterative selection procedures (TISP) by She (2009). Using thresholding rules rather than penalty functions we make our approach greatly facilitates the computation and the analysis. Our simulation shows that the newly proposed method compare favorably with other variable selection techniques. Furthermore, it can be applied to most existing sufficient dimension reduction methods and possibly to inverse regression estimators based on minimum discrepancy functions.